OICC Press Communications in Nonlinear Analysis 2371-7920 13 1 2025 06 30 Benefaction of Rothe's Time Discretization Method to Solve Diffusion Equation Involving Riemann-Liouville Fractional Integral and Delay Integral Function 26 36 10.57647/cna.2025.bcr2-d739 EN Nishi Gupta Department of Mathematics,Indian Institute of Technology Guwahati,Assam India https://orcid.org/0000-0003-3111-8418 Journal Article 2025 06 30 This paper presents a diffusion equation involving $\alpha^{th}$ order Riemann-Liouville (R-L) fractional integral along with integral forcing function for delay and some constant coefficients. We apply $L2$ scheme to discretize the fractional integral function and Rothe's method  is opted to establish the existence and uniqueness of a strong solution. In addition, we provide some error estimation and continuous on initial data. Eventually, we provide an application to manifest the results.